Express each of the complex number given in the Exercises 1 to 10 in the form a + ib :
(- 2 - 1/3i)³

Solution:

The given complex number is,

(- 2 - 1/3i)³ = (- 1)³ (2 + 1/3i)³

= - [2³ + (i/3)³ + 3 (2) (i/3) (2 + i/3)]

= - [8 + i³/27 + 2i (2 + i/3)]

= - [8 - i/27 + 4i + 2/3 i²] [∵ i³ = - i]

= - [8 - i/27 + 4i - 2/3] [∵ i² = - 1]

= - [22/3 + 107/27 i]

= - 22/3 - i (107/27)

NCERT Solutions Class 11 Maths Chapter 5 Exercise 5.1 Question 10

Express each of the complex number given in the Exercises 1 to 10 in the form a + ib : (- 2 - 1/3i)³

Summary:

A complex number is given. We have expressed the given complex number in the standard form to be - 22/3 - i (107/27)